Sounds like you have some issue with the old Mac or a compatibility issue of some sort. Try booting the new Mac into Safe Mode which will prevent the automatic launching of third party software during boot & login. If Safe Mode allows you to boot, then some third party software is most likely the problem. You can try running EtreCheck and posting the report here using the "Additional Text" icon which looks like a piece of paper so we can see if any known offenders are on you Mac. Typical culprits are anti-virus apps, cleaning/optimizer apps, and third party security software...none of which are needed on a Mac.
If Safe Mode does not allow you to boot the Mac, then your best option is to perform a clean install of macOS by using Recovery Mode. If you cannot access Recovery Mode, then performing a "Restore" of the firmware may be necessary which requires access to another Mac running macOS 10.15+.
After performing a clean install or firmware "Restore", you can attempt to migrate again, but only migrate your macOS user accounts. Leave all the other options unchecked (you can probably also allow "other folder") since most likely the issue is due to third party apps or a system setting. Of course there is still a slim possibility you will have the same issue...if so, then start over once more, but this time manually create a new macOS user account using Setup Assistant. After logging into your new Mac, launch the Time Machine app and restore the items from the TM backup. If you don't have a TM backup, then you should create a TM backup of your old Mac. Otherwise you will need to manually transfer all your data from the old Mac either using File Sharing or a USB3 SSD, or possibly Target Disk Mode.
People should always have frequent and regular backups of their computer and all external media (including the cloud) which contains important & unique data. Not having a backup means the data is not important and you can live without the data.